Despite the widely touted benefits of omega-3 fatty acids for preserving cognitive function and memory, a new review by the Cochrane Library finds that those effects may be overstated: healthy elderly people taking omega-3 supplements did no better on tests of thinking and verbal skills than those taking placebo.

A number of previous studies have associated omega-3 consumption with better brain health and a lower risk of Alzheimer’s disease. One recent study by Columbia University researchers found that people who ate diets higher in omega-3s had lower blood levels of beta amyloid, the telltale protein that gums up brains in Alzheimer’s patients. In another study published in the journal Neurology in February, researchers showed that people with the highest levels of omega-3s in their blood had bigger brain volumes and performed better on tests of visual memory and abstract reasoning, compared with those with the lowest levels.

Much of this previous data has been observational, however. So, for the Cochrane review, researchers looked specifically at so-called “gold standard” studies, those that randomly assigned people to take either omega-3s or a placebo and then tracked the participants over time. The authors of the review, from the London School of Hygiene & Tropical Medicine, included three studies involving a total of 3,536 people over the age of 60, which lasted between six and 40 months. All the participants started the studies in good cognitive health.

In two studies, researchers compared the effects of omega-3 (fish oil) capsules versus placebo capsules containing olive or sunflower oil. In the third study, participants used either omega-3-fortified margarine or a regular margarine spread. In the end, the data showed that participants who got extra omega-3s performed no better on standard tests of mental abilities, memory or verbal fluency than those who took placebos.

“Our analysis suggests that there is currently no evidence that omega-3 fatty acid supplements provide a benefit for memory or concentration in later life,” says study co-author Alan Dangour, a nutritionist at the London School of Hygiene & Tropical Medicine. “We hope that people will use this new evidence to help inform their decisions on dietary supplement use.”

Still, it’s possible that the cognitive benefits of omega-3s may take longer than a few years — longer than the studies included in the review lasted — to show up. Cognitive decline and dementia may take several years to develop, and researchers saw very little mental decline in any of the study participants, so further research is needed to suss out the longer-term effects of omega-3 supplementation.

It’s also possible that taking omega-3 supplements may help only those who are low in the fatty acid to start with, while offering less benefit for those who already get enough through their regular diets.

None of this is to say that a diet naturally high in omega-3s — from fish, for example — isn’t good for your health. The authors recommend that people eat two portions of fish a week, including one portion of oily fish. “The evidence of health benefits from the consumption of omega-3 fatty acids is strongest for heart health, but there may also be other health benefits,” says Dangour.

What’s good for the heart is also good for the brain, researchers say, so there are plenty of lifestyle changes you can make to help protect your cognitive health as you age: get regular exercise, eat well and keep your weight and blood pressure down.